Common fixed points of generalized Meir-Keeler α-contractions

Abstract

Motivated by Abdeljawad (Fixed Point Theory Appl. 2013:19, 2013, we establish some common fixed point theorems for three and four self-mappings satisfying generalized

Applying new fixed point theorems on fractional and ordinary differential equations

“…On the other hand, by using fixed point theorems, the existence and uniqueness of solutions to differential/integral equations involving fractional operators were studied by a huge number of researchers. With respect to this issue, we refer to [26][27][28][29][30][31][32][33][34][35] and the references cited in those articles.…”

(α,ψ)-Meir-Keeler Contraction Mappings in Generalized b-Metric Spaces

“…for all , V ∈ N 0 . By (15) and the fact that ∈ Ψ, it follows that { } is a Cauchy sequence of elements of . Since is complete, there exists ∈ with lim →∞ ( , ) = 0.…”

“…This result has been generalized and extended in many directions; see [5][6][7][8][9][10][11][12][13][14][15]. Using some auxiliary functions, the main purpose of this paper is to extend and generalize this result on generalized -metric spaces.…”

Generalized weakly α-contractive mappings and applications to ordinary differential equations

“…The basic idea of this principle rests in the use of successive approximations to establish the existence and uniqueness of solution of an operator equation f .x/ D x, particularly it can be employed to prove the existence of solution of differential or integral equations. Due to its applications in mathematics and other related disciplines, Banach contraction principle has been generalized in many directions (for example, see [1,[3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21].…”